Showing posts with label Yr10-Math. Show all posts
Showing posts with label Yr10-Math. Show all posts
Wednesday, 28 August 2019
Wednesday, 21 August 2019
A comprehensive review of trigonometry
1. What are some of the mathematical concepts we have looked at or worked on in class?
I opted to study trigonometry in maths, so a small group of us have looked at Pythagoras theorem and the concept of SAH, CAH, and TOA in trig. I didn't have any experience with any of these concepts when I first started but I've definitely improved a lot. I'm really enjoyed trigonometry so far as it kind of (emphasis on kind of) relates to algebra which is one concept of mathematics that I really, really like and am relatively good at.
What questions do you still have about trig?
Honestly the question I want answered is how can I get better. I really enjoy some aspects of maths and want to continue into vocational or enterprise maths in NCEA next year, plus trig is pretty useful to know if I want to be successful in this subject. I'm confident in everything we've learned so far through the worksheets we've been given as well as the independent study time we're given.
3. Describe a mistake or misconception you or a classmate had in class. What did you learn from this mistake?
One mistake I made was with the calculator, I had no idea how to make the cos/sin/tan with the little exponent come up (turns out it's shift + cos,sin,or tan) but I asked for help and learned from it. Any other mistakes I made, I googled and got some pretty good answers but asking Mr Werder for help gave me a lot more specific help for a certain equation.
4. What new vocab words were introduced?
Sin, cos, tan were always words I saw on my calculator but I never knew the meaning of, now I know what they mean and can use them in my work confidently. Pythagoras theorem was new to me too, as for trig I recognised the word but didn't know what work it covered. So, I've learned a lot of new words so far.
PSA:
The following resources helped me enormously with my work in trig. I would recommend to anyone who wants to learn more about the use of SAH, CAH, and TOA.
https://www.youtube.com/watch?v=2umc214GSkY&t=322s
https://www.youtube.com/watch?v=Bx_7PckdjxA
I opted to study trigonometry in maths, so a small group of us have looked at Pythagoras theorem and the concept of SAH, CAH, and TOA in trig. I didn't have any experience with any of these concepts when I first started but I've definitely improved a lot. I'm really enjoyed trigonometry so far as it kind of (emphasis on kind of) relates to algebra which is one concept of mathematics that I really, really like and am relatively good at.
What questions do you still have about trig?
Honestly the question I want answered is how can I get better. I really enjoy some aspects of maths and want to continue into vocational or enterprise maths in NCEA next year, plus trig is pretty useful to know if I want to be successful in this subject. I'm confident in everything we've learned so far through the worksheets we've been given as well as the independent study time we're given.
3. Describe a mistake or misconception you or a classmate had in class. What did you learn from this mistake?
One mistake I made was with the calculator, I had no idea how to make the cos/sin/tan with the little exponent come up (turns out it's shift + cos,sin,or tan) but I asked for help and learned from it. Any other mistakes I made, I googled and got some pretty good answers but asking Mr Werder for help gave me a lot more specific help for a certain equation.
4. What new vocab words were introduced?
Sin, cos, tan were always words I saw on my calculator but I never knew the meaning of, now I know what they mean and can use them in my work confidently. Pythagoras theorem was new to me too, as for trig I recognised the word but didn't know what work it covered. So, I've learned a lot of new words so far.
PSA:
The following resources helped me enormously with my work in trig. I would recommend to anyone who wants to learn more about the use of SAH, CAH, and TOA.
https://www.youtube.com/watch?v=2umc214GSkY&t=322s
https://www.youtube.com/watch?v=Bx_7PckdjxA
Wednesday, 15 May 2019
Thursday, 28 March 2019
A Recap of Week 9 Maths
Week 9 Maths Recap
1. What were the main mathematical concepts or ideas that you learned about or that we discussed in class?
We discussed circumferences of circles, scientific notation, speed, and distance.
3. What new vocab words or terms were introduced?
Diameter, circumference, Pi, radius, scientific notation - I didn't know/hadn't heard of these words beforehand, but now that I confidently know all of them I'm pretty proud of myself.
In recent weeks, 10Sp has been learning about numerous areas (no pun intended) of mathematics with Mr. Werder, and I decided I'd share some with you. Not only did I learn a few things that I had no idea of, I extended my knowledge further on things I already knew at least a tiny aspect of.
An example of a maths problem we did in our groups:
"Tennis balls come in a tube of three, typically. If you were to measure it out, what is bigger - the height of the tube or the diameter of the tube?"
Out of everything we've done this was my favourite because we were provided with helpful examples, some questions to ask, and I feel as if my group (consisting of Josh, Jnaya, Natasha and myself) really worked together well to work out the problem, and were able to understand it thoroughly.
Using terms we'd learned in previous weeks on Mathletics and group problems with Mr Werder, we were able to work out the diameter of the tennis ball. Natasha had the idea of tracing around the ball so we easily did that.
The diameter, if you didn't know is the space between one side to another. In this case, we discovered the tennis ball's circumference was 7 cm. When measuring the diameter it was vital that we measured from the widest part of the ball (the very centre) to ensure it was accurate.
We determined the next step was to work out the height of the tube. This was very simple in my opinion. There were 3 7x7 balls in the tube, meaning we simply had to multiple 3 x (3 balls, 7cm in diameter) to find the height of the tube. 3x 7 is 21. The height of the tube is 21cm.
To explain it a bit further, to work out the circumference, use this formula.
If you are unfamiliar with Pi, it is equal to 3.14, and the symbol looks like this: π. Derived from the Ancient Greek letter Pi.
Now, time to answer the question. Which is bigger, the diameter of the tennis ball tube, or the height of the tennis ball tube?
To answer this we had to find the circumference using the formula above.
C= 3.14 x 7 = 21.98cm
(Circumference = 3.14 (Pi) multipled by 7 (7cm is the diameter of the tennis ball) = 21.98cm is the circumference of the tennis ball tube.)
From there we were able to determine that the circumference of the tube is bigger. This is because 3 x 7 (21) is smaller than 3.14 x 7 (21.98). Therefore the circumference would always be bigger than the height in instances where there is three balls/objects stacked like tennis balls in a tube, even if it was three enormous planets stacked up in a tube, the circumference of the tube would always be bigger because 3.14 is bigger than 3.
If you'd like to explore more of the maths work we did, here is a compilation of the problems we solved in our groups. Leave a comment if you worked one out, or leave some feedback if you'd like me to explain any of them further.
Have a good day!
1. What were the main mathematical concepts or ideas that you learned about or that we discussed in class?
We discussed circumferences of circles, scientific notation, speed, and distance.
3. What new vocab words or terms were introduced?
Diameter, circumference, Pi, radius, scientific notation - I didn't know/hadn't heard of these words beforehand, but now that I confidently know all of them I'm pretty proud of myself.
In recent weeks, 10Sp has been learning about numerous areas (no pun intended) of mathematics with Mr. Werder, and I decided I'd share some with you. Not only did I learn a few things that I had no idea of, I extended my knowledge further on things I already knew at least a tiny aspect of.
An example of a maths problem we did in our groups:
"Tennis balls come in a tube of three, typically. If you were to measure it out, what is bigger - the height of the tube or the diameter of the tube?"
Out of everything we've done this was my favourite because we were provided with helpful examples, some questions to ask, and I feel as if my group (consisting of Josh, Jnaya, Natasha and myself) really worked together well to work out the problem, and were able to understand it thoroughly. Using terms we'd learned in previous weeks on Mathletics and group problems with Mr Werder, we were able to work out the diameter of the tennis ball. Natasha had the idea of tracing around the ball so we easily did that.
The diameter, if you didn't know is the space between one side to another. In this case, we discovered the tennis ball's circumference was 7 cm. When measuring the diameter it was vital that we measured from the widest part of the ball (the very centre) to ensure it was accurate.
We determined the next step was to work out the height of the tube. This was very simple in my opinion. There were 3 7x7 balls in the tube, meaning we simply had to multiple 3 x (3 balls, 7cm in diameter) to find the height of the tube. 3x 7 is 21. The height of the tube is 21cm.
To explain it a bit further, to work out the circumference, use this formula.
If you are unfamiliar with Pi, it is equal to 3.14, and the symbol looks like this: π. Derived from the Ancient Greek letter Pi.
Now, time to answer the question. Which is bigger, the diameter of the tennis ball tube, or the height of the tennis ball tube?
To answer this we had to find the circumference using the formula above.
C= 3.14 x 7 = 21.98cm
(Circumference = 3.14 (Pi) multipled by 7 (7cm is the diameter of the tennis ball) = 21.98cm is the circumference of the tennis ball tube.)
From there we were able to determine that the circumference of the tube is bigger. This is because 3 x 7 (21) is smaller than 3.14 x 7 (21.98). Therefore the circumference would always be bigger than the height in instances where there is three balls/objects stacked like tennis balls in a tube, even if it was three enormous planets stacked up in a tube, the circumference of the tube would always be bigger because 3.14 is bigger than 3.
If you'd like to explore more of the maths work we did, here is a compilation of the problems we solved in our groups. Leave a comment if you worked one out, or leave some feedback if you'd like me to explain any of them further.
Have a good day!
Monday, 11 February 2019
YOUCUBED PROGRAMME RECAP
The Importance of Struggle from YouCubed on Vimeo.
During our first two weeks of Year 10 math with Mr Werder, we have been watching and taking part in the YouCubed programme, run by Jo Boaler from Stanford University. YouCubed provides a series of fun videos explaining encouraging facts about maths and the human brain.
"Struggle is important" is one of these facts. I learnt that when you are working on a difficult maths problem, this is actually creating or strengthening pathways in your brain which ultimately make you better at math itself. I really enjoyed learning about this because more times than not, when I faced with a difficult problem, I tend to sometimes give up or enlist help in somebody else. Now I have motivation to actually complete maths problems and not give up, knowing that it's actually making my brain stronger, which is something I think everyone should strive to achieve at my age.
During our first two weeks of Year 10 math with Mr Werder, we have been watching and taking part in the YouCubed programme, run by Jo Boaler from Stanford University. YouCubed provides a series of fun videos explaining encouraging facts about maths and the human brain.
"Struggle is important" is one of these facts. I learnt that when you are working on a difficult maths problem, this is actually creating or strengthening pathways in your brain which ultimately make you better at math itself. I really enjoyed learning about this because more times than not, when I faced with a difficult problem, I tend to sometimes give up or enlist help in somebody else. Now I have motivation to actually complete maths problems and not give up, knowing that it's actually making my brain stronger, which is something I think everyone should strive to achieve at my age.
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